%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET767+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:36:56 AM UTC 2026
% Result : Theorem 73.15s 10.73s
% Output : CNFRefutation 73.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 5 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 42 ( 15 ~; 13 |; 9 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 38 ( 2 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(equivalence_class,axiom,
! [R,E,A,X] :
( member(X,equivalence_class(A,E,R))
<=> ( apply(R,A,X)
& member(X,E) ) ),
file('theBenchmark.p',equivalence_class) ).
fof(thIII03,conjecture,
! [E,R,A] :
( equivalence(R,E)
=> subset(equivalence_class(A,E,R),E) ),
file('theBenchmark.p',thIII03) ).
fof(thIII03_neg,negated_conjecture,
~ ! [E,R,A] :
( equivalence(R,E)
=> subset(equivalence_class(A,E,R),E) ),
inference(assume_negation,[status(cth)],[thIII03]) ).
fof(nnf_17,plain,
? [E,R,A] :
( ~ subset(equivalence_class(A,E,R),E)
& equivalence(R,E) ),
inference(fof_nnf,[status(thm)],[thIII03_neg]) ).
fof(sk_thIII03_neg,plain,
( ~ subset(equivalence_class(sK0,sK1,sK2),sK1)
& equivalence(sK2,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK1,sK0]),skolemize(E,sK1),skolemize(R,sK2),skolemize(A,sK0)],[nnf_17]) ).
cnf(c_218,negated_conjecture,
~ subset(equivalence_class(sK0,sK1,sK2),sK1),
inference(split_conjunct,[status(thm)],[sk_thIII03_neg]) ).
cnf(c_221,plain,
( member(A,C)
| ~ member(A,equivalence_class(B,C,D)) ),
inference(clausify,[status(thm)],[equivalence_class]) ).
fof(nnf_1,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[subset]) ).
fof(sk_subset_sk,plain,
! [A,B] :
( ( ( ~ member(sK3(A,B),B)
& member(sK3(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X,sK3(A,B))],[nnf_1]) ).
fof(sk_subset,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK3(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK3(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_subset_sk]) ).
cnf(c_245,plain,
( ~ member(sK3(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_246,plain,
( member(sK3(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_876,plain,
member(sK3(equivalence_class(sK0,sK1,sK2),sK1),equivalence_class(sK0,sK1,sK2)),
inference(resolve,[status(thm)],[c_246,c_218]) ).
cnf(c_4805,plain,
member(sK3(equivalence_class(sK0,sK1,sK2),sK1),sK1),
inference(resolve,[status(thm)],[c_876,c_221]) ).
cnf(c_4963,plain,
subset(equivalence_class(sK0,sK1,sK2),sK1),
inference(resolve,[status(thm)],[c_4805,c_245]) ).
cnf(c_4962,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_218,c_4963]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET767+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 08:13:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.39 % Process 1666491 was started by sandbox on n005,
% 0.11/0.39 % Sat Sep 26 08:13:32 2026
% 0.11/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 73.15/10.73
% 73.15/10.73 % given #500 (I,wt=47): 613 -member(A,B) | -member(f14(B,C),B) | -member(f16(B,C),B) | -apply(C,A,f14(B,C)) | -apply(C,f14(B,C),f16(B,C)) | apply(C,A,f16(B,C)) | member(f11(B,C),B) | member(f12(B,C),B). [factor(255,e,i)].
% 73.15/10.73
% 73.15/10.73 % SZS status Theorem for theBenchmark
% 73.15/10.73
% 73.15/10.73 % Proof 1 at 1.51 (+ 0.55) seconds.
% 73.15/10.73 % Length of proof is 10.
% 73.15/10.73 % Level of proof is 4.
% 73.15/10.73 % Maximum clause weight is 17.000.
% 73.15/10.73 % Given clauses 901.
% 73.15/10.73
% 73.15/10.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------